Difference between revisions of "orch:Solvers"

Revision as of 17:32, 7 March 2016

Chemical kinetics

This chapter reports the principles that drive the computation of combustion chemistry in most CFD softwares.

Chemkin (.scheme .therm .trans), Cantera (xml)

...

Arrhenius law

${\displaystyle {\mathcal {A}}_{j}}$ is the pre-exponential factor, ${\displaystyle {\mathcal {\beta }}_{j}}$ is the temperature exponent and ${\displaystyle E_{a_{j}}}$ the activation energy

${\displaystyle k_{j}={\mathcal {A}}_{j}T^{{\mathcal {\beta }}_{j}}\exp \left(-{\frac {E_{a_{j}}}{RT}}\right)}$

Three-body reactions

In the forward direction, three-body reactions involve two species A and B as reactants and yield a single product AB. In that case, the third body M is used to stabilize the excited product AB*. On the contrary, in the reverse direction, heat provides the energy necessary to break the link between A and B.

${\displaystyle ......}$

The third body M can be any inert molecule.

Falloff reactions

Under specific conditions, some reaction rate expressions are dependent on pressure and temperature. This is especially true for the rate associated to unimolecular/recombination fall-off reactions which increases with pressure. In such cases, if the chemical process takes place in a high or low pressure limit

    <!-- reaction 0012    -->
    <reaction reversible="yes" type="falloff" id="0012">
      <equation>O + CO (+ M) [=] CO2 (+ M)</equation>
      <rateCoeff>
        <Arrhenius>
           <A>1.800000E+07</A>
           <b>0</b>
           <E units="cal/mol">2385.000000</E>
        </Arrhenius>
        <Arrhenius name="k0">
           <A>6.020000E+08</A>
           <b>0</b>
           <E units="cal/mol">3000.000000</E>
        </Arrhenius>
        <efficiencies default="1.0">AR:0.5  C2H6:3  CH4:2  CO:1.5  CO2:3.5  H2:2  H2O:6  O2:6 </efficiencies>
        <falloff type="Lindemann"/>
      </rateCoeff>
      <reactants>CO:1 O:1.0</reactants>
      <products>CO2:1.0</products>
    </reaction>
</code>

=== Reaction rates ===

The global rate of a reaction j (evolution in concentration per unit of time) varies depending on the proportion of the rates associated to the forward and backward directions. 

<math>
	\mathcal{Q}_j = \mathcal{Q}_{f,j} - \mathcal{Q}_{r,j} 
</math>


=== Production/Consumption source terms ===

Species <math>Y_k</math> source terms are deduced from 

<math>
	\dot{\omega}_k = W_k \sum_{j=1}^{N_R} \nu_{k,j} \mathcal{Q}_j
</math>

== Solver to build reference trajectories ==

== DRGEP solver for species reduction ==

* Compute species direct inter-relations

* Compute species relations through indirect paths

* Compute relations between targets and

== DRGEP solver for reactions reduction ==



== QSS solver ==

* Solve for thermodynamic

<math>h_k = \Delta h_{f,k}^{0} + h_{sk}</math>

<math>h_{sk} = \int_{T_0}^{T} Cp_k dT</math>

Get Gibbs Free Energy

Get Equilibrium constants